Trigonometry Problems and Questions with Solutions - Grade 10

Find the lengths of all sides of the right triangle below if its area is 400.

BH is perpendicular to AC. Find x the length of BC.

ABC is a right triangle with a right angle at A. Find x the length of DC.

In the figure below AB and CD are perpendicular to BC and the size of angle ACB is 31o. Find the length of segment BD.

The area of a right triangle is 50. One of its angles is 45o. Find the lengths of the sides and hypotenuse of the triangle.

In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).

In a right triangle ABC with angle A equal to 90o, find angle B and C so that sin(B) = cos(B).

A rectangle has dimensions 10 cm by 5 cm. Determine the measures of the angles at the point where the diagonals intersect.

The lengths of side AB and side BC of a scalene triangle ABC are 12 cm and 8 cm respectively. The size of angle C is 59o. Find the length of side AC.

From the top of a 200 meters high building, the angle of depression to the bottom of a second building is 20 degrees. From the same point, the angle of elevation to the top of the second building is 10 degrees. Calculate the height of the second building.

Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30o. The balloon rises 50 meters. Now the angle of depression to the car is 35 degrees. How far is the car from point P?

If the shadow of a building increases by 10 meters when the angle of elevation of the sun rays decreases from 70o to 60o, what is the height of the building?